Question

A plane glass mirror of thickness $3cm$of material of $\mu=\dfrac{3}{2}$ is silvered on the back surface. When a point object is placed $9cm$ from the front surface of the mirror, then the position of the brightest image from the front surface is
A. $9cm$
B. $11cm$
C. $12cm$
D. $13cm$

Answer 1

Hint: The given question consists of the combination of a thin slab and a mirror.
Hence there will be an apparent shift given by $t\prime=\dfrac{t}{\mu}$. And distance of the image from the non-silver face will be, distance of image – distance of the reflection of the object

Formula used: Apparent shift is given by $t\prime=\dfrac{t}{\mu}$

Complete step-by-step solution -
The given question consists of the combination of a thin slab and a mirror.
Given that, the thickness of the slab $t=3cm$
Refractive index of the slab $\mu=\dfrac{3}{2}$
Then the apparent shift is given by $t\prime=\dfrac{t}{\mu}=\dfrac{3}{\dfrac{3}{2}}=2$
Given that, the object is placed at a distance $9cm$
Due to the shift, the object is placed at a distance $9+2=11cm$
Since one side of the slab is coated, it acts as a mirror. If the object is place at $11cm$, then the image is obtained at $11+11=22cm$
Distance of the image from the non-silver face will be, distance of image – distance of the reflection of the object ie.$22-9=13cm$ .
Hence , the answer is D.$13cm$

Additional Information:
Mirror reflects or bounces back, only a fraction of the beam of light in a single direction, as compared to other objects which either scatter light or absorb it. They are used to see one's reflection, like the normal mirror we use in house, or are used to see objects that are not visible directly, like rear mirrors and dentist’s mirror. There are various types of mirrors on the basis of shapes, like plane mirrors , the ones we use generally, which provide real images and curved mirrors, which may distort or magnify the image, generally seen in mirror mazes.

Note: Mirror reflects or bounces back, only a fraction of the beam of light in a single direction. Since the slab of certain thickness is silvered on one side, it acts a system of mirror and slab. When light passes through a slab of certain thickness it results in an apparent shift of the image.